Question

Suppose that X is a normal random variable and E(X) = −3. Find Var(X) if P(−7 < X < 1) = 0.7888.

Answer 1

For normal distribution, P(X < A) = P(Z < (A - )/)

E(X), = -3

Var(X), ² = ?

P(-7 < X < 1) = 0.7888

-3 is the midpoint of the interval (-7, 1) and it is the mean of the distribution.

Therefore P(-7 < X < -3) = P(-3 < X < 1) = 0.7888/2 = 0.3944

P(-3 < X < 1) = 0.3944

P(X < 1) - P(X < -3) = 0.3944

P(Z < (1 - -3)/) + 0.5 = 0.3994

P(Z < 4/) = 0.8994

Take the z score corresponding to 0.8994 from standard normal distribution table

4/ = 1.28

= 3.125

² = 3.13² = 9.8

Var(X) = 9.8